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Re: Three piece function

  • To: mathgroup at
  • Subject: [mg60250] Re: Three piece function
  • From: Paul Abbott <paul at>
  • Date: Thu, 8 Sep 2005 04:53:45 -0400 (EDT)
  • Organization: The University of Western Australia
  • References: <dfm7fi$h87$>
  • Sender: owner-wri-mathgroup at

In article <dfm7fi$h87$1 at>,
 "Steven Jonak" <JonakSt at> wrote:

> I'm a little new to using Mathematica for creating handouts/quizzes and
> tests so please bear with me!  I'm using Mathematica to write a test and
> I can't seem to get a decent looking three-piece function.  For two
> pieces, the typesetting palette works fine.  I used Show Expression to
> see how they got the curly bracket on the left side but when I tried to
> change it to three pieces with a curly bracket on the left side (a one
> row, three column matrix with the bracket) the size of the bracket
> doesn't change--and looks bad.

By a three-piece function (sounds like a suit), I assume you mean a 
piecewise function? The Mathematica function Piecewise[] is built-in to 
handle this -- and has built-in typesetting rules. For example,

  f[x_] := Piecewise[{{x, x > 0}, {1, x == 0}, {-x, x < 0}}]

is such a function, and

  HoldForm[f[x]] == f[x] // TraditionalForm

gives you the formatted function. This is the easy way -- using 
Mathematica's typsetting to do the job for you.

There is a way to change the size of a spanning bracket -- and this was 
covered by Neil Soiffer in the Tricks of the Trade column of The 
Mathematica Journal 8(1):

Very large brackets and braces for their common uses in Mathematica 
(function call, lists) can look silly. Hence, as defined in, they are set to grow to at most "2.01" (factor of 
two, with a fudge factor) times their normal size when SpanMaxSize is 
set to Automatic. Spanning can be controlled by selecting 

  Expression Input | Spanning Characters | Expand Indefinitely 

from the Edit menu. Alternatively, if you use the Option Inspector and 
type in Span you will see the Spanning Character Options. You can set 
SpanMaxSize around the character, at the cell level, notebook level, or 
globally. You may not be happy with what the brackets and braces look 
like for function calls and lists, though. Here is the result of setting 
SpanMaxSize -> Infinity at the character level.

There is another problem: in each case the opening bracket is displayed 
in color, indicating that it is unmatched. In TraditionalForm, a better 
alternative is to close off the unmatched left bracket with 
\[AutoRightMatch] (or \[EscapeKey]\right.\[EscapeKey]) which keeps 
things properly bracketed. This will not work for StandardForm unless 
you set DelimiterMatching->None for the cell (or any larger scope). Here 
is the result of closing off the unmatched left bracket.


Paul Abbott                                      Phone:  61 8 6488 2734
School of Physics, M013                            Fax: +61 8 6488 1014
The University of Western Australia         (CRICOS Provider No 00126G)    

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